Problem: Solve for $x$ and $y$ using elimination. ${3x-2y = -6}$ ${-5x-5y = -65}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $3$ ${15x-10y = -30}$ $-15x-15y = -195$ Add the top and bottom equations together. $-25y = -225$ $\dfrac{-25y}{{-25}} = \dfrac{-225}{{-25}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {3x-2y = -6}\thinspace$ to find $x$ ${3x - 2}{(9)}{= -6}$ $3x-18 = -6$ $3x-18{+18} = -6{+18}$ $3x = 12$ $\dfrac{3x}{{3}} = \dfrac{12}{{3}}$ ${x = 4}$ You can also plug ${y = 9}$ into $\thinspace {-5x-5y = -65}\thinspace$ and get the same answer for $x$ : ${-5x - 5}{(9)}{= -65}$ ${x = 4}$